Question

if D E and F are the midpoints of sides BC CA and ab respectively of triangle ABC whose vertices are a - 4, 1 D 6, 7 and c 2 ,- 9 then prove that area of triangle d e f is equal to 1 by 4 area of triangle ABC

Answer 1

The triangle formed by mid pts is always 1/4th the area of triangle

But if you are able to do than, first find the coordinates of triangle by applying mid pt. formula and find all the coordinates.

Then find the area of triangle ABC by area formula and also of triangle DEF

When compare both the areas you will get the result